Exercise 3.2: Value and Zeros of a Polynomial

Exercise 3.2

1. Find the value of the polynomial f ( y) = 6y − 3y² + 3 at

(i) y = 1 (ii) y = –1 (iii) y = 0

2. If p(x) = x²– 2√2x +1, find p(2√2) .

3. Find the zeros of the polynomial in each of the following :

(i) p(x) = x – 3 (ii) p(x) = 2x + 5 (iii) q(y) = 2y – 3 (iv) f(z) = 8z (v) p(x) = ax when a ≠ 0 (vi) h ( x) = ax + b , a ≠ 0, a , b ∈ R

4. Find the roots of the polynomial equations .

(i) 5x – 6 = 0

(ii) x +3 = 0

(iii) 10x + 9 = 0

(iv) 9x – 4 = 0

5. Verify whether the following are zeros of the polynomial indicated against them, or not.

(i) p (x) = 2x − 1, x = 1/2 (ii) p(x) = x³ − 1, x = 1  (iii) p(x) = ax + b, x = − b/a (iv) p(x) = ( x + 3) (x – 4), x = 4 , x = –3

6. Find the number of zeros of the following polynomials represented by their graphs.

Solution: